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Quantum Electronics

Numerical simulation of nonstationary effects of radiation polarisation for the Λ interaction scheme in the case of degenerate energy levels

А. В. Волков, Oleg M. Parshkov, Дружинина Надежда Александровна

Published Sep 30, 2009• 4 citations
Publisher

Abstract

Nonstationary polarisation effects in a medium with the Λ-scheme of energy levels with the quantum numbers of the total angular momentum equal to 0, 2, and 1 are numerically simulated. The analysis is performed in the slowly varying envelope approximation taking into account the inhomogeneous broadening of quantum transition lines. It is assumed that the lower-frequency (signal) radiation at the input to a resonance medium is considerably weaker than the higher-frequency (pump) radiation. It is shown that the polarisation of the signal pulse inside the medium is quasi-elliptic in the general case and is independent of the input-pulse polarisation. If the 'area' of the input pump pulse in the absence of signal radiation admits the formation of only one 2π-pulse, then the major axes of polarisation ellipses for the signal inside the medium and input pump radiation are collinear, however, the directions of rotation of the electric field strengths of these radiations are mutually opposite. For higher-power pump pulses, the polarisation structure of the signal pulse in the medium becomes considerably more complicated.

DOI
10.1070/qe2009v039n09abeh013935

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Quantum Electronics•Aug 31, 2005•0 citations
Nonstationary polarisation effects in a medium with the Λ-scheme of energy levels with the quantum numbers of the total angular momentum equal to 0, 2, and 1 are numerically simulated. The analysis is performed in the slowly varying envelope approximation taking into account the inhomogeneous broadening of quantum transition lines. It is assumed that the lower-frequency (signal) radiation at the input to a resonance medium is considerably weaker than the higher-frequency (pump) radiation. It is shown that the polarisation of the signal pulse inside the medium is quasi-elliptic in the general case and is independent of the input-pulse polarisation. If the 'area' of the input pump pulse in the absence of signal radiation admits the formation of only one 2π-pulse, then the major axes of polarisation ellipses for the signal inside the medium and input pump radiation are collinear, however, the directions of rotation of the electric field strengths of these radiations are mutually opposite. For higher-power pump pulses, the polarisation structure of the signal pulse in the medium becomes considerably more complicated.
The nonstationary double resonance is numerically simulated in the Λ-scheme of degenerate energy levels with the quantum number J of the total angular momentum equal to 0, 2, and 1. The analysis is performed in the slowly varying envelope approximation taking into account the inhomogeneous broadening of quantum transition lines. In the case of a high-power input low-frequency pulse of long duration with a flat top switched on before the application of a comparatively weak and short input high-frequency pulse and switched off after the end of the latter, a specific pulsed structure, the so-called double adiabaton, can appear. It differs from an adiabaton known from the theory of electromagnetically induced transparency by the decomposition of the high-frequency pulse into two pulses with oppositely directed elliptic polarisations.
We report the results of numerical simulation of the evolution of a weak elliptically polarised input probe pulse in the case of electromagnetically induced transparency in the field of elliptically polarised control light. It is shown that the electric field strength of any input probe pulse can be represented as a sum of the electric field strengths of two subpulses whose polarisation ellipses have the same constant eccentricities and mutually perpendicular directions of the major axes, one of these axes being parallel to the major axis of the polarisation ellipse of the control light. The directions of rotation of the electric field strength vectors of subpulses are mutually opposite. Subpulses move with different velocities in a medium, which leads to their spatial separation. In the propagation of subpulses, their polarisation characteristics (eccentricities and directions of major axes of polarisation ellipses) remain unchanged. At any stage of evolution, including the instants of significant spatial overlapping of subpulses, the intensity of the probe light in the medium is the sum of their intensities. Consequently, these subpulses are nonstationary mutually orthogonal elliptically polarised normal modes of the probe field whose existence is related to the medium anisotropy caused by the control field. The simulation is carried out for a scheme of degenerate quantum transitions between 3 P 0 , 3 P 1 0 and 3 P 2 levels of the 208 Pb isotope, taking into account the Doppler broadening of the spectral lines under the assumption that the probe field has a higher frequency than the control field.
An analysis is made of the coherent interaction of a short pulse of polarised electromagnetic radiation with a medium in which the energy levels are degenerate in respect of the angular momentum projection. In the case of the j a = 1 → j b =0 transition it is found, without recourse to the approximation of slowly varying envelopes, that the system of the Maxwell–Bloch equations has an exact solution in the form of a steady-state solitary wave of duration equal to half the period of emission as a result of the investigated atomic transition. A new solution is obtained, in addition to a simple generalisation corresponding to a polarised video pulse. When the populations of the excited states with different projections of the angular momentum are different, the spherical components of the vector representing the electric field intensity do not behave proportionately: if one of them corresponds to a unipolar spike of the electric field, the other component is a variable-sign solitary wave.
The evolution of adiabatons in electromagnetically induced transparency in the scheme of degenerate quantum transitions with Doppler broadening of spectral lines has been numerically simulated taking into account the effect of resonance detunings. It is shown that, in the case of linearly polarised fields, an increase in the probe-field resonance detuning (under exact-resonance conditions for the control radiation) leads to a transformation of electromagnetically induced transparency into electromagnetically induced absorption at certain stages. When the control-field resonance detuning is varied, the transparency of the medium for the probe (exactly resonant) radiation monotonically decreases with increasing detuning because of the rising role of single-photon absorption. In the case of circularly polarised control radiation and linearly polarised input probe field, a probe pulse propagating in the medium splits into two pulses with oppositely directed circular polarisations. An increase in the probe pulse resonance detuning (under exact-resonance conditions for the control radiation) leads primarily to an increase in the absorption by the medium of the probe pulse, the direction of circular polarisation for which coincides with the circular-polarisation direction for the control radiation.
Abstract We report the results of a theoretical study of the evolution of a probe pulse under electromagnetically induced transparency conditions in the lambda scheme of degenerate inhomogeneously broadened quantum transitions. It is assumed that the interacting fields are elliptically polarised, and their effect on the medium can be either strictly resonant or quasi-resonant. It is shown that probe light in a medium can be represented as the sum of two normal modes, i.e. quasi-monochromatic elliptically polarised fields propagating independently of each other. The major axis of the polarisation ellipse of the normal mode of the first type is parallel, and that of the second type is perpendicular to the major axis of the polarisation ellipse of the control light. Due to the fact that velocities of normal-mode pulses are different, a single probe pulse entering a medium splits into individual pulses inside the medium, each of which transfers the energy of one of the normal modes. In the case of quasi-resonance, the splitting occurs at a shorter distance than in the case of strict resonance. If normal modes are not phase modulated at the input surface of the medium, then in the case of quasi-resonance they become phase modulated during their propagation inside the medium, whereas this does not occur in the case of strict resonance. It is shown that in the case of quasi-resonance, the phase modulation value of the mode of the second of the above types significantly exceeds that of the first type. The medium transparency for the normal mode of the first type slightly decreases with the transition from the case of strict resonance to the case of quasi-resonance, while the medium transparency for the mode of the second type decreases significantly. The total probe field, which is the sum of the normal modes, has phase modulation before it splits into mode pulses in cases of both strict resonance and quasi-resonance, even if it does not have it on the input surface.
The transient double resonance in the Λ scheme is numerically investigated in the case of a strong inhomogeneous spectral broadening of a medium and nonzero detunings of the frequencies of interacting pulses from the central frequencies of corresponding quantum transitions. It is shown that the signal pulse efficiently interacts with the pump pulse only when a certain condition imposed on the nonzero detunings is satisfied. If this condition is strongly violated at the input to the resonance medium, only a weak field of the rear edge of the input signal pulse mainly interacts with the pump field. In this case, two pulses with different frequencies are formed in the signal channel. This is explained by the specific interaction of radiation with Doppler-broadened quantum transitions.